On frames for Krein spaces
A definition of frames for Krein spaces is proposed, which extends the notion of ℐ-orthonormal bases of Krein spaces. A ℐ-frame for a Krein space (ℋ,[,]) is in particular a frame for ℋ in the Hilbert space sense. But it is also compatible with the indefinite inner product [ , ], meaning that it dete...
Guardado en:
| Autores principales: | , , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2012
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83926 |
| Aporte de: |
| Sumario: | A definition of frames for Krein spaces is proposed, which extends the notion of ℐ-orthonormal bases of Krein spaces. A ℐ-frame for a Krein space (ℋ,[,]) is in particular a frame for ℋ in the Hilbert space sense. But it is also compatible with the indefinite inner product [ , ], meaning that it determines a pair of maximal uniformly ℐ-definite subspaces, an analogue to the maximal dual pair associated to a ℐ-orthonormal basis. Also, each ℐ-frame induces an indefinite reconstruction formula for the vectors in ℋ, which resembles the one given by a ℐ-orthonormal basis. |
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